My son is working his way through the Geometric Approach and we've been greatly appreciative to have Dr. Cotter herself help guide us in email form. We've now come to Lesson 69 (pages 78-79) and are a bit confused. What is the purpose of Step 2 on page 79? We have no difficulties in measuring 1 cm (10 mm) or 1.3 cm (13 mm), etc. from the edges of the signs, but what is the reasoning for sliding the 45 degree triangle to get two more lines that are perpendicular to the original lines? These eventually intersect at the same point. Is it just so we have a bigger "dot" to line up with the mmArc Compass(TM) so it is more accurate?

Also--With the second worksheet (69-2), how are we to accurately draw the 70 degree point at the bottom of the arrow. (We figured that the other angles should be 55 degrees because there are 180 degrees in a triangle.) The materials needed for this lesson did not include a goniometer so we assumed that we needed to draw it without the aid of such a device.

I hope my questions are clear. Thank you in advance for helping guide us!

Hi, Lori!

If I am understanding your first question correctly, you need to draw the parallel lines so you know where toe begin and end the arc. After you draw the arc, you can erase the 'extra' lines.

With your second question, I pretty much just use whatever equipment I need - even when it is not listed in the 'Materials' section. In fact, I didn't even notice that it was not in the 'Materials' section until you said so. :-) I suppose I should read a little more closely! Either way, Dr. Cotter want the students to figure out the problem and use whatever tools are necessary to get the answer. The way you accomplish the answer might be different from someone else. That is the beauty of this program! It makes the student figure it out and 'think outside the box'.

I hope that has addressed your questions. If not, you can email me at rachel@rightstartmath.com or at info@rightstartmath.com.

Have a wonderful day!